Bannon had been summoned to testify before the congressional panel reviewing the riot on Thursday.
He did not come, urging the head of the committee to set a Tuesday vote to hold him in criminal contempt.
If sentenced, Bannon faces a fine and up to one year in prison. Democrats say he is trying to postpone the probe.
Bannon, a conservative media executive who became Trump's leading tactician, was dismissed from the White House in 2017 and was not in government at the time of the January riot.
He has been asked to testify about his conversation with Trump a week before the incident - as well as his involvement in reviewing plans to reverse the election results that saw Joe Biden win the White House.
Mr. Trump's supporters charged the Capitol building in Washington, DC on January 6 in a lost attempt to overturn the certification of Biden's victory. Hundreds of Mr. Trump's supporters have since been seized for their actions that day.
Subpoena papers cited Bannon as saying "all hell is going to break loose tomorrow" on the eve of the riot, which left five dead.
Bannon has repeatedly said he has no intentions of arriving before the board.
He has contended that executive privilege, which shields some presidential communications, protects his talks with Mr. Trump. Mr. Bannon's lawyers say he will proceed to oppose until a court has ruled on the matter.
Democrats claim that Bannon is employing a delaying tactic to push back proceedings until after the midterm elections in November 2022, which may change the power tension in the House of Representatives, the lower chamber of Congress.
On Tuesday, the Democratic-led investigative committee will decide whether to refer the contempt charge for a total House vote.
House lawmakers would then have to rule on whether Mr. Bannon is in contempt. If the Democratic-majority House votes yes, the case will be referred to the Department of Justice for criminal prosecution.
While this development is not remarkable, with Democrats controlling both Congress and the presidency, this may be a rare instance where a congressional contempt charge has some teeth.
It also comes as the Democratic base requests accountability for the Trump administration's actions, calling on their members in Congress to flex their oversight muscles.
In August, the House probing committee asked for records relating to the day's events, including communications from Trump, members of his family, his top aides, his lawyers, and other former members of his administration.